Acoustic tools are useful in providing a large range of information regarding formation and borehole parameters adjacent the tools. A primary use of acoustic borehole measurements is for estimating compressional and/or shear wave formation slowness. Formation slowness is not measured directly but rather is determined from the various acoustic waveforms received by the receivers. Formation slowness is often measured by placing an array of sensors in a sonde in a borehole, the array including at least one transmitter and at least one receiver; transmitting an acoustic signal from the transmitter; receiving the acoustic signal with the receiver; and calculating the formation slowness considering the distance between the transmitter and receiver and the time between transmission of the signal by the transmitter and signal receipt at the receiver. Calculating the formation slowness is complex however as many different acoustic types of signals are received in response to a transmitted signal. A single transmitted acoustic signal, whether monopole, dipole, quadrapole, or multipole, can generate a variety of waves in a borehole environment that are received by the receivers. To process the acoustic data, it is necessary to separate and classify the various received waves into general waveform categories such as compressional, shear and Stoneley arrivals.
One method to estimate formation slowness is the slowness-time coherence (STC) method wherein the semblance peaks of the waveforms received by the sensor array are located in a slowness-time plane. U.S. Pat. No. 4,594,691 describes STC processing and is incorporated herein in its entirety. Certain received signals, such as those generated by the dipole flexural mode, are dispersive. For dispersive modes, a dispersive variation of STC processing, such as Dispersive STC (DSTC) processing as described in U.S. Pat. No. 5,278,805 and QDSTC as described in U.S. Pat. No. 5,587,966, each of which are incorporated herein in their entirety, is useful when processing dispersive acoustic data. One particular use of STC processing is to determine the compressional and shear slowness of the formation.
STC semblance processing facilitates the determination of slowness for various components propagating across an array of sonic waveforms. The result of semblance processing is normally represented in a two-dimensional time-slowness map (time vs. slowness). The result of semblance processing is normally presented versus depth by projecting the time-slowness map onto the slowness axis according to the following equation:
            P      i        ⁡          (      s      )        =            max      t        ⁢                  ρ        i            ⁡              (                  S          ,          t                )            
where Pi is the slowness projection, and                pi is the semblance computed at each level, which is a function of the slowness, S, and time, t.        
In STC processing, a window or band in the slowness-time plane is identified with each type of arrival. In order to minimize the effect of parameter uncertainty in dispersive STC, the processing band is dynamically adjusted depending on the stacking slowness and the measured borehole diameter, taking the sensitivity to these parameters into account. Although robust and useful, DSTC processing has limitations. Basic assumptions in DSTC processing are that borehole formations are homogeneous, isotropic formations and that the tool effects in the received signals owing to the presence of the tool in the borehole can be easily addressed. As advances are made in borehole acoustic tools and processing of sonic logging data, these assumptions may be revisited.
In dipole sonic logging, a flexural wave moves through the borehole fluid and along the borehole wall at a rate dependent upon the velocity of the borehole fluid (i.e. mud slowness) and the shear slowness of the formation. The flexural mode is also sensitive to other parameters such as borehole diameter, densities and compressional slowness of the formation. These parameters need to be considered but their exact values may be difficult to determine. The lack of precise values for the parameters means that the final slowness estimation will also include some degree of uncertainty. Furthermore, these can vary throughout the borehole logging, making it inaccurate to apply a uniform value or correction throughout a logged interval.
In evaluating sonic data, it would be useful to provide a measure of the degree of uncertainty in the final slowness estimation. The present invention is directed toward a method of determining dispersion factors in dipole sonic logging and the sensitivity of the calculated formation shear slowness to such factors. In particular, the present invention provides methods to determine the sensitivity of the flexural mode slowness to the formation shear slowness in dipole acoustic logging.
Additional advantages and novel features of the invention will be set forth in the description which follows or may be learned by those skilled in the art through reading these materials or practicing the invention. The advantages of the invention may be achieved through the means recited in the attached claims.